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Looking at we can see that the first term is and the last term is where the coefficients are 1 and -10 respectively.
Now multiply the first coefficient 1 and the last coefficient -10 to get -10. Now what two numbers multiply to -10 and add to the middle coefficient -9? Let's list all of the factors of -10:
Factors of -10:
1,2,5,10
-1,-2,-5,-10 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -10
(1)*(-10)
(2)*(-5)
(-1)*(10)
(-2)*(5)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9
First Number
Second Number
Sum
1
-10
1+(-10)=-9
2
-5
2+(-5)=-3
-1
10
-1+10=9
-2
5
-2+5=3
From this list we can see that 1 and -10 add up to -9 and multiply to -10
Now looking at the expression , replace with (notice adds up to . So it is equivalent to )
Now let's factor by grouping:
Group like terms
Factor out the GCF of out of the first group. Factor out the GCF of out of the second group
Since we have a common term of , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
(